@natalierose127
I'm going to throw a little confusion into this discussion. There is probably no other plant that is so steeped in conflicting information as lavender, starting with the naming. Both Lavandula dentata and L. stoechas are both sold as French lavender and both are sold under different names also. There is a L. x intermedia "Provence" than many people assume is "French" lavender because of the name. My point is that it helps to know what you've got. I'm not seeing L. dentata in your photos, but perhaps I just can't discern the detail of the toothed leaves.
You've made a good choice with the soil, but I'm not sure about the pot. If that saucer is attached to the pot, it prevents it from freely draining. Your best choice is a pot with a large hole, and don't use a saucer at all.
As with everything Lavender, "rules" about feeding and watering are all over the place. Remember that a confined plant in sterile potting oil needs supplementary feeding. And because its roots can't stretch out to find water underground, it needs more from you. Sources conflict about nitrogen, but I think MG is too high. Since your goal is to get it bushier, I would worry less right now about getting it to bloom and concentrate on overall vigor. MG flushes through pretty fast, so I would start giving it diluted fish emulsion (5-1-1) every week. Water first, let it absorb into the soil, then water again with the fish. Sometime in the fall, feed it with something close to a 5-7-3. (that happens to be the NPK proportions of a Happy Frog fertilizer I have. Doesn't need to be exact, but the N should not be higher than the P. A 10-10-10 could work, but at half strength). It will probably be in dry, rather than liquid, form: it doesn't matter which, just go lighter rather than heavier.
Your climate is hot but with high-ish humidity--as I type this, your humidity is 61%, mine is 17%
so we need to allow for that. Still, I think you should increase the water. Here's one way to find out if you're under/over-watering: Water it as you usually do, wait two days, then pull the whole thing, soil and all, out of the pot and check the moisture at the bottom. If it's soggy, your drainage is poor and that's a whole other can of worms. If the bottom is dry but the top is damp, you need to water more deeply. If it's uniformly damp throughout the pot, fine. Water exactly like that roughly every week while it's very hot. All of this is variable. You might go 10 days. Here's the takeaway:>>> The frequency of watering is less important than the drainage<<< Lavenders don't like wet feet.
I am drawing on my own experience and research, both on the internet and in my various reference books, and the commonly held "rule" that you must not cut into the woody stem is disputed and, in my recent experience, not true. Late last fall I tucked a large healthy potted lavender in a sheltered place on the patio to protect it from freezing and forgot about it, so it didn't get watered. In March I pulled it out and it looked entirely dead. I had hacked off most of the branches to make it easier to lug to the trash barrel when I noticed tiny green buds all over the woody base. I pulled it out of the pot, trimmed some roots, refreshed the soil, fed and watered it. It is still a pathetic specimen and needs another year to fully come back, but it grew and bloomed profusely. I wish I'd taken photos of that process. Here is what it grew from--as I say, I had just hacked at it:
I read somewhere that some lavenders will sprout from wood and some won't, but darn, I don't know which ones and can't find that source
So I'd play it safe and prune as Gerald suggested, above, but watch for new growth below. If it does sprout from the wood, you can get more aggressive next year. You'll want to do a lighter trim in early spring before the buds form. I do know that in your area "spring" can be in February. Just watch for new growth.
Sorry to ramble on. If this were any other plant, it would have taken one paragraph. Here are a couple of sources I found, and they have conflicting advice (to each other and to me!). Sometimes it just takes trial and error.
https://www.gardenanswersmagaz...
https://www.hortzone.com/blog/...
Good luck!